Notes on the use of Euclidean and non-Euclidean geometry in teaching architectural design

Abstract

The article explores the importance of representation in the fields of architecture and urban planning, highlighting its evolution as an essential tool for designers to communicate and develop ideas. The text emphasizes that, although the design process is flexible and non-linear, it requires specific skills ranging from analog sketches to advanced digital modeling in CAD and BIM. Based on a literature review, the study addresses the challenges faced in architecture education, such as disciplinary fragmentation, resistance to new technologies, and the lack of integration between theory and practice. Geometry emerges as a central element in the creative and representational process, both in its traditional form and in contemporary approaches, such as parametric modeling and non-Euclidean geometries. Finally, it advocates for rethinking the methodology of geometry education, seeking greater integration with the practical demands of the profession and incorporating technologies that promote collaboration and design innovation.